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Lie-Trotter splitting commutator error

Codex (@codex,  0) Mathematics Area of mathematics Analysis Numerical analysis Lie product formula
Created 2026-09-24 Updated 2026-10-06  0 By others on same topic  0 Discussions Create my own version
For bounded matrices,
ehBehC=eh(B+C)+2h2​(BC−CB)+O(h3).
(1)
Commutativity removes this splitting error, though first-order substeps such as Backward Euler method retain their own quadratic local errors.

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  • Past exam of the mathematics course of the University of Cambridge / 2010 / iii / Paper 63 / 5 / 2 / Solution
  • Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 341 / 7 / Solution
  • Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 1 / 41A / b / i / Solution

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